Nonadiabatic electron dynamics

F. Rebentrost, C. Figl, R. Goldmann, O. Hoffmann, D. Spelsberg, J. Grosser, Nonadiabatic electron dynamics in the exit channel of Na-molecule optical colhsions. J. Chem. Phys. 128, 224307 (2008)... 

One possible way to treat chemical dynamics in a large molecular system involved with nonadiabatic electron dynamics is to divide the system into the electron mixing part and the rest. Methodologies in multiscale physics... 

We track the nonadiabatic electron dynamics from HO-CH=NH to 0=CH-NH2. Main findings through study are as follows, (i) This dynamics... 

Many things have been thus clarified in the above simple analysis of the onedimensional projection of the potential energy surfaces. We then proceed to the study of nonadiabatic electron dynamics based on the full-dimensional nuclear paths that are nonadiabatically coupled with electrons. Although we have studied the cases of three- and five-membered ammonia clusters, we mainly report the tri-ammonia case in what follows. 

Fig. 7.34 Snapshots of the Schiff current of probability (electron flux) in the nonadiabatic electron dynamics, (a) at the moment of transfer from phenol to ammonia cluster, (b) and (c) further fluctuation of the flux within the ammonia cluster. (Reprinted with permission from K. Nagashima et ai, J. Phys. Chem. A 116, 11167 (2012)).

Through the above analysis based on nonadiabatic electron dynamics, it has been clarified ... 

Prom the methodological view point, we would like to emphasize that the nonadiabatic electron dynamics in the branching path representation or its approximation SET is indeed necessary and useful to comprehend the dynamics of such highly quasi-degenerate electronic systems. 

In this minimal END approximation, the electronic basis functions are centered on the average nuclear positions, which are dynamical variables. In the limit of classical nuclei, these are conventional basis functions used in moleculai electronic structure theoiy, and they follow the dynamically changing nuclear positions. As can be seen from the equations of motion discussed above the evolution of the nuclear positions and momenta is governed by Newton-like equations with Hellman-Feynman forces, while the electronic dynamical variables are complex molecular orbital coefficients that follow equations that look like those of the time-dependent Hartree-Fock (TDHF) approximation [24]. The coupling terms in the dynamical metric are the well-known nonadiabatic terms due to the fact that the basis moves with the dynamically changing nuclear positions. 

The author would like to thank all the group members in the past and present who carried out all the researches discussed in this chapter Drs. C. Zhu, G. V. Mil nikov, Y. Teranishi, K. Nagaya, A. Kondorskiy, H. Fujisaki, S. Zou, H. Tamura, and P. Oloyede. He is indebted to Professors S. Nanbu and T. Ishida for their contributions, especially on molecular functions and electronic structure calculations. He also thanks Professor Y. Zhao for his work on the nonadiabatic transition state theory and electron transfer. The work was supported by a Grant-in-Aid for Specially Promoted Research on Studies of Nonadiabatic Chemical Dynamics based on the Zhu-Nakamura Theory from MEXT of Japan. 

Samanta, A. A., and S. K. Gosh. 1995. Density functional approach to the solvent effects on the dynamics of nonadiabatic electron transfer reactions. J. Chem. Phys. 102, 3172. 

Following earlier workby Warshel, Halley and Hautman"" and Curtiss etal presented an approximate numerical scheme to calculate the nonadiabatic electron transfer rate under the above conditions. The method is based on solving Eq. (18) to the lowest order in the coupling F by treating the elements Hj and as known functions of time obtained from the molecular dynamics trajectories. The result for the probability of the system making a transition to the final state at time t, given that it was in the initial state at time fo. is given by... 

Figure 3. Time-dependent simulations of the nonadiabatic photoisomerization dynamics exhibited by Model III, comparing results of the mean-field-trajectory method (dashed lines), the surface-hopping approach (thin lines), and exact quanmm calculations (full lines). Shown are the population probabilities of the initially prepared (a) adiabatic and (b) diabatic electronic state, respectively, as well as (c) the probability Pdsit) that the sytem remains in the initially prepared cis conformation.

To summarize, the results presented for five representative examples of nonadiabatic dynamics demonstrate the ability of the MFT method to account for a qualitative description of the dynamics in case of processes involving two electronic states. The origin of the problems to describe the correct long-time relaxation dynamics as well as multi-state processes will be discussed in more detail in Section VI. Despite these problems, it is surprising how this simplest MQC method can describe complex nonadiabatic dynamics. Other related approximate methods such as the quantum-mechanical TDSCF approximation have been found to completely fail to account for the long-time behavior of the electronic dynamics (see Fig. 10). This is because the standard Hartree ansatz in the TDSCF approach neglects all correlations between the dynamical DoF, whereas the ensemble average performed in the MFT treatment accounts for the static correlation of the problem. 

Because the mapping approach treats electronic and nuclear dynamics on the same dynamical footing, its classical limit can be employed to study the phase-space properties of a nonadiabatic system. With this end in mind, we adopt a onemode two-state spin-boson system (Model IVa), which is mapped on a classical system with two degrees of freedom (DoF). Studying various Poincare surfaces of section, a detailed phase-space analysis of the problem is given, showing that the model exhibits mixed classical dynamics [123]. Furthermore, a number of periodic orbits (i.e., solutions of the classical equation of motion that return to their initial conditions) of the nonadiabatic system are identified and discussed [125]. It is shown that these vibronic periodic orbits can be used to analyze the nonadiabatic quantum dynamics [126]. Finally, a three-mode model of nonadiabatic photoisomerization (Model III) is employed to demonstrate the applicability of the concept of vibronic periodic orbits to multidimensional dynamics [127]. 

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